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The authors observe a characteristic Page curve associated with a maximally entangled, highly scrambled, but globally pure state.
“We observe a characteristic Page curve51 associated with a maximally entangled, highly scrambled, but globally pure state.”
From Logical quantum processor based on reconfigurable atom arrays (2024) · cites this paper as [51]
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Cites
Average entropy of a subsystem
Page, D. N. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1291 · Cited by 1,578 · see citing works
Black holes as mirrors: quantum information in random subsystems
Hayden, P., & Preskill, J. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/09/120 · Cited by 1,332 · see citing works
Horowitz, G. T., & Strominger, A. (1991) · Nuclear Physics B · doi:10.1016/0550-3213(91)90440-9 · Cited by 1,178 · see citing works
The stretched horizon and black hole complementarity
Susskind, L., Thorlacius, L., & Uglum, J. (1993) · Physical Review D · doi:10.1103/physrevd.48.3743 · Cited by 1,081 · see citing works
Self-citationBlack holes: The membrane paradigm
Thorne, K. S., Price, R. H., & Macdonald, D. A. (2010) · Medical Entomology and Zoology · Cited by 1,046 · see citing works
Supergravity and the large N limit of theories with sixteen supercharges
Nissan Itzhaki, A., MALDACENA, J. M., Jacob Sonnenschein, B., & Shimon Yankielowicz, B. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.046004 · Cited by 948 · see citing works
The Holographic Bound in Anti-de Sitter Space
Susskind, L., & Witten, E. (1998) · arXiv · doi:10.48550/arxiv.hep-th/9805114 · Cited by 604 · see citing works
Self-citationD-branes and Short Distances in String TheoryPreprint
Douglas, M. R., Kabat, D., Pouliot, P., & Shenker, S. H. (1996) · Cited by 445 · see citing works
Random Quantum Circuits are Approximate 2-designs
Harrow, A. W., & Low, R. A. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0873-6 · Cited by 324 · cited 1× · see citing works
“See [8] for the study of more general cases and for subtleties of the definition of scrambling.”
BackgroundGedanken experiments involving black holes
Susskind, L., & Lárus Thorlacius, A. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.966 · Cited by 198 · see citing works
Self-citationA matrix model for black hole thermalization
Iizuka, N., & Polchinski, J. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/10/028 · Cited by 74 · see citing works
Matrix models for the black hole information paradox
Iizuka, N., Okuda, T., & Polchinski, J. (2010) · Journal of High Energy Physics · doi:10.1007/jhep02(2010)073 · Cited by 51 · see citing works
Semiclassical geometry of charged black holes
Frolov, A. V., Kristjansson, K. R., & Lárus Thorlacius, A. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.72.021501 · Cited by 24 · see citing works
Global geometry of two-dimensional charged black holes
Frolov, A. V., Kristjansson, K. R., & Lárus Thorlacius, A. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.124036 · Cited by 19 · see citing works
Exact and Approximate Unitary 2-Designs: Constructions and ApplicationsPreprint
Dankert, C., Cleve, R., Emerson, J., & Livine, E. R. (2006) · HAL · Cited by 9 · see citing works
The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
Festuccia, G., & Liu, H. (2006) · CERN Document Server (European Organization for Nuclear Research) · doi:10.48550/arxiv.hep-th/0611098 · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- [5]5. D. Kabat and P. Pouliot, Comment on zero-brane quantum mechanics, Phys. Rev. Lett. 77 (1996) 1004 [hep-th/9603127]; · arXiv
- [6]6. U.H. Danielsson, G. Ferretti and B. Sundborg, D-particle dynamics and bound states, Int. J. Mod. Phys. A 11 (1996) 5463 [hep-th/9603081]; · arXiv
- [8]8. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043]. · arXiv
- [15]15. L. Susskind and J.S. Lindesay, Black holes, information, and the string theory revolution: the holographic universe, World Scientific, Singapore (2005).
Cited by
Sorted by citations
Black Holes: Complementarity or Firewalls?
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2012) · arXiv · doi:10.48550/arxiv.1207.3123 · Cited by 1,471
Black holes: complementarity or firewalls?
Almheiri, A., Marolf, D., Polchinski, J., & Sully, J. (2013) · Journal of High Energy Physics · doi:10.1007/jhep02(2013)062 · Cited by 1,470 · see citing works
Logical quantum processor based on reconfigurable atom arrays
Bluvstein, D., Evered, S. J., Geim, A. A., Li, S. H., Zhou, H., Manovitz, T., Ebadi, S., Cain, M., Kalinowski, M., Hangleiter, D., et al. (2024) · Nature · doi:10.1038/s41586-023-06927-3 · Cited by 1,119 · see citing works
The entropy of Hawking radiation
Almheiri, A., Hartman, T., Maldacena, J., Shaghoulian, E., & Tajdini, A. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.035002 · Cited by 706 · see citing works
“The time scale r s log S BH is called “the scrambling time” and it has an interesting significance that we will not discuss in this review, see e.g. [68, 69].”
Shenker, S. H., & Stanford, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep05(2015)132 · Cited by 604 · see citing works
Black holes and random matrices
Cotler, J. S., Gur-Ari, G., Hanada, M., Polchinski, J., Saad, P., Shenker, S. H., Stanford, D., Streicher, A., & Tezuka, M. (2017) · Journal of High Energy Physics · doi:10.1007/jhep05(2017)118 · Cited by 562 · see citing works
Jerusalem lectures on black holes and quantum information
Harlow, D. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.015002 · Cited by 480 · see citing works
Almheiri, A., Marolf, D., Polchinski, J., Stanford, D., & Sully, J. (2013) · Journal of High Energy Physics · doi:10.1007/jhep09(2013)018 · Cited by 425 · see citing works
Local Random Quantum Circuits are Approximate Polynomial-Designs
Brandão, F. G. S. L., Harrow, A. W., & Horodecki, M. (2016) · Communications in Mathematical Physics · doi:10.1007/s00220-016-2706-8 · Cited by 404 · see citing works
Time dependence of Hawking radiation entropy
Page, D. N. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/09/028 · Cited by 354 · see citing works
An infalling observer in AdS/CFT
Papadodimas, K., & Raju, S. (2013) · Journal of High Energy Physics · doi:10.1007/jhep10(2013)212 · Cited by 335 · see citing works
Information scrambling in quantum circuits
Mi, X., Roushan, P., Quintana, C., Mandrà, S., Marshall, J., Neill, C., Arute, F., Arya, K., Atalaya, J., Babbush, R., et al. (2021) · Science · doi:10.1126/science.abg5029 · Cited by 283 · see citing works
On the dynamics of near-extremal black holes
Nayak, P., Shukla, A., Soni, R. M., Trivedi, S. P., & Vishal, V. (2018) · Journal of High Energy Physics · doi:10.1007/jhep09(2018)048 · Cited by 206 · see citing works
The black hole information problem: past, present, and future
Marolf, D. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa77cc · Cited by 205 · see citing works
Scrambling the spectral form factor: Unitarity constraints and exact results
del Campo, A., Molina-Vilaplana, J., & Sonner, J. (2017) · Physical Review D · doi:10.1103/physrevd.95.126008 · Cited by 133 · see citing works
Barren Plateaus Preclude Learning Scramblers
Holmes, Z., Arrasmith, A., Yan, B., Coles, P. J., Albrecht, A., & Sornborger, A. T. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.190501 · Cited by 125 · see citing works
Direct Randomized Benchmarking for Multiqubit Devices
Proctor, T. J., Carignan-Dugas, A., Rudinger, K., Nielsen, E., Blume-Kohout, R., & Young, K. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.030503 · Cited by 118 · see citing works
Spread of entanglement in a Sachdev-Ye-Kitaev chain
Gu, Y., Lucas, A., & Qi, X.-L. (2017) · Journal of High Energy Physics · doi:10.1007/jhep09(2017)120 · Cited by 109 · see citing works
Learning the Alpha-bits of black holes
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Unitarity and fuzzball complementarity: “Alice fuzzes but may not even know it!”
Avery, S. G., Chowdhury, B. D., & Puhm, A. (2013) · Journal of High Energy Physics · doi:10.1007/jhep09(2013)012 · Cited by 70 · see citing works
Holographic spacetime, black holes and quantum error correcting codes: a review
Kibe, T., Mandayam, P., & Mukhopadhyay, A. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10382-1 · Cited by 44 · see citing works
Onset of Scrambling as a Dynamical Transition in Tunable-Range Quantum Circuits
Kuriyattil, S., Hashizume, T., Bentsen, G., & Daley, A. J. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.030325 · Cited by 5 · see citing works
- Authors
- Sekino, Y., & Susskind, L.
- Affiliations
- Okayama Institute for Quantum Physics (JP)
- Stanford University (US)
- Venue
- Journal of High Energy Physics
- Published
- 2008-10-15
- Volume
- 2008
- Issue
- 10
- Pages
- 065-065
- ISSN
- 1029-8479 (ISSN-L)
- OpenAlex
- W3037318174
- Cited by
- 1,112
- References
- 16
- Citations by year
- 2026: 67 · 2025: 118 · 2024: 105 · 2023: 114 · 2022: 117 · 2021: 93 · 2020: 100 · 2019: 94 · 2018: 78 · 2017: 58 · 2016: 53 · 2015: 26 · 2014: 25 · 2013: 30 · 2012: 10
- FWCI
- 4.45
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of High Energy Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- quantum scrambling, thermalization, scrambling time, matrix quantum mechanics, black holes, quantum chaos, logarithmic scaling
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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